<i>n</i>-<i>K</i>-Increasing Aggregation Functions
We introduce and discuss the concept of <i>n</i>-ary <i>K</i>-increasing fusion functions and <i>n</i>-ary <i>K</i>-increasing aggregation functions, <i>K</i> being a subset of the index set <inline-formula><math xmlns="http:/...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-11-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/12/12/1065 |
| _version_ | 1797382071771987968 |
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| author | Radko Mesiar Anna Kolesárová Adam Šeliga Radomír Halaš |
| author_facet | Radko Mesiar Anna Kolesárová Adam Šeliga Radomír Halaš |
| author_sort | Radko Mesiar |
| collection | DOAJ |
| description | We introduce and discuss the concept of <i>n</i>-ary <i>K</i>-increasing fusion functions and <i>n</i>-ary <i>K</i>-increasing aggregation functions, <i>K</i> being a subset of the index set <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>{</mo><mn>1</mn><mo>,</mo><mo>…</mo><mo>,</mo><mi>n</mi><mo>}</mo></mrow></semantics></math></inline-formula> indicating in which variables a considered function is increasing. It is also assumed that this function is decreasing in all other variables. We show that each <i>n</i>-ary <i>K</i>-increasing aggregation function is generated by some aggregation function which enables us to introduce and study the properties of <i>n</i>-ary <i>K</i>-increasing aggregation functions related to the properties of their generating aggregation functions. In particular, we also discuss binary <i>K</i>-increasing aggregation functions, including fuzzy implication and complication functions, among others. |
| first_indexed | 2024-03-08T21:01:11Z |
| format | Article |
| id | doaj.art-f6acb6f6fdd549bf9556ab0f635098d4 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-08T21:01:11Z |
| publishDate | 2023-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-f6acb6f6fdd549bf9556ab0f635098d42023-12-22T13:53:08ZengMDPI AGAxioms2075-16802023-11-011212106510.3390/axioms12121065<i>n</i>-<i>K</i>-Increasing Aggregation FunctionsRadko Mesiar0Anna Kolesárová1Adam Šeliga2Radomír Halaš3Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Slovak University of Technology, Radlinského 11, 810 05 Bratislava, SlovakiaDepartment of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Slovak University of Technology, Radlinského 11, 810 05 Bratislava, SlovakiaDepartment of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Slovak University of Technology, Radlinského 11, 810 05 Bratislava, SlovakiaDepartment of Algebra and Geometry, Faculty of Science, Palacký Univeristy Olomouc, 771 46 Olomouc, Czech RepublicWe introduce and discuss the concept of <i>n</i>-ary <i>K</i>-increasing fusion functions and <i>n</i>-ary <i>K</i>-increasing aggregation functions, <i>K</i> being a subset of the index set <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>{</mo><mn>1</mn><mo>,</mo><mo>…</mo><mo>,</mo><mi>n</mi><mo>}</mo></mrow></semantics></math></inline-formula> indicating in which variables a considered function is increasing. It is also assumed that this function is decreasing in all other variables. We show that each <i>n</i>-ary <i>K</i>-increasing aggregation function is generated by some aggregation function which enables us to introduce and study the properties of <i>n</i>-ary <i>K</i>-increasing aggregation functions related to the properties of their generating aggregation functions. In particular, we also discuss binary <i>K</i>-increasing aggregation functions, including fuzzy implication and complication functions, among others.https://www.mdpi.com/2075-1680/12/12/1065aggregation functionfusion function<i>n</i>-<i>K</i>-increasing aggregation function<i>n</i>-<i>K</i>-increasing fusion function |
| spellingShingle | Radko Mesiar Anna Kolesárová Adam Šeliga Radomír Halaš <i>n</i>-<i>K</i>-Increasing Aggregation Functions Axioms aggregation function fusion function <i>n</i>-<i>K</i>-increasing aggregation function <i>n</i>-<i>K</i>-increasing fusion function |
| title | <i>n</i>-<i>K</i>-Increasing Aggregation Functions |
| title_full | <i>n</i>-<i>K</i>-Increasing Aggregation Functions |
| title_fullStr | <i>n</i>-<i>K</i>-Increasing Aggregation Functions |
| title_full_unstemmed | <i>n</i>-<i>K</i>-Increasing Aggregation Functions |
| title_short | <i>n</i>-<i>K</i>-Increasing Aggregation Functions |
| title_sort | i n i i k i increasing aggregation functions |
| topic | aggregation function fusion function <i>n</i>-<i>K</i>-increasing aggregation function <i>n</i>-<i>K</i>-increasing fusion function |
| url | https://www.mdpi.com/2075-1680/12/12/1065 |
| work_keys_str_mv | AT radkomesiar iniikiincreasingaggregationfunctions AT annakolesarova iniikiincreasingaggregationfunctions AT adamseliga iniikiincreasingaggregationfunctions AT radomirhalas iniikiincreasingaggregationfunctions |